Lenses typically have two shaped surfaces that concentrate or disperse electromagnetic waves, such as light. Each lens refracts (or bends) electromagnetic waves that pass through the lens, similar to the way a prism refracts light. Each lens is made out of an optically transparent or translucent material, such as glass or plastic. The refractive index of the lens material and curvature of the shaped surfaces define the refraction of the electromagnetic waves.
Lenses can be found in a broad range of applications including illumination optics and imaging optics. In illumination optics, a lens confines or directs light from a light source into a beam to direct the light into an intended area of illumination. For example, a lens can direct light from an office ceiling lamp in a cubicle to the work area in the cubicle, and not other work areas in other cubicles.
In imaging optics, a lens confines or directs light from an object image to the focal plane of the lens. The light in the focal plane of the lens can be captured on film or with an electronic imaging sensor, such as a charge coupled device (CCD) or complementary metal oxide semiconductor (CMOS) imaging device.
Digital imaging systems, such as digital picture cameras, digital video cameras, and optical navigation mice, are sampled data systems. These sampled data systems include one or more lenses and one or more electronic imaging sensors for capturing an object image. The electronic imaging sensors include photo detectors that sample the object image. If spatial frequencies in the object image are greater than half the spatial sampling frequency of the electronic imaging sensor, the spatial frequency information exceeds the Nyquist frequency for the digital imaging system and aliasing errors can occur. For example, the electronic imaging sensor may sample the object image at a sample rate of 100 samples per millimeter (mm). If spatial frequencies in the object image are greater than 50 samples per mm, the spatial frequency information exceeds the Nyquist frequency for the digital imaging system and aliasing errors can occur.
Lenses are typically not perfect. Each lens includes aberrations that reduce the sharpness of images viewed through the lens. As a result, each lens operates as a low pass filter that reduces the magnitude of high spatial frequency information passing through the lens, where high spatial frequency information corresponds to fine image detail and a sharper image. The spatial frequency response of a lens is referred to as the lens' modulation transfer function (MTF), which is the contrast at a given spatial frequency relative to the contrast at other spatial frequencies. Lenses in digital imaging systems that pass high spatial frequency information contribute to aliasing errors in the digital imaging system.
One type of anti-aliasing filter includes birefringent material, such as crystalline structures. The birefringent material refracts light in two directions to blur the object image and filter high spatial frequency information. However, anti-aliasing filters that include birefringent material can be expensive.
For these and other reasons there is a need for the present invention.